|Peter Boettke|

Over at EconLog, my dear friend and colleague Bryan Caplan is channeling Alfred Marshall's (Burn the Mathematics) and Murray Rothbard's (Occam's razor) critiques of the overuse and misuse of mathematical modeling in the discipline of economics. I am no doubt biased, but all my intellectual sympathies are with Caplan on this issue. And I believe his proposed test actually is a very good one.

To remind the young aspiring economists readers of the arguments, Marshall in 1906 wrote that he had "a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules - (1) Use mathematics as a shorthand language, rather than an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can't succeed in (4), burn (3). This last I did often."

And Murray Rothbard, at least in part, argued in *Man, Economy, and State* that the dance of thinking through the economic intuition, translating it into math, then translating it back into English to explain was a violation of the philosophical and scientific principle of Occam's razor. But Rothbard did go further in his criticism, as he put it: "Aside from doing no more than verbal logic can do, and therefore violating the scientific principle of Occam’s razor—that science should be as simple and clear as possible—such a use of mathematics contains grave errors and defects within itself. In the first place, it cannot describe the path by which the economy approaches the final equilibrium position. This task can be performed only by verbal, logical analysis of the causal action of human beings. It is evident that this task is the important one, since it is this analysis that is significant for human action. Action moves along a path and is not describable in an unchanging, evenly rotating world. The world is an uncertain one, and we shall see shortly that we cannot even pursue to its logical conclusion the analysis of a static, evenly rotating economy. The assumption of an evenly rotating economy is only an auxiliary tool in aiding us in the analysis of real action. Since mathematics is least badly accommodated to a static state, mathematical writers have tended to be preoccupied with this state, thus providing a particularly misleading picture of the world of action."

Economics, mid-20th century, took a turn toward excessive formalism and excessive aggregation, and as a discipline it hasn't fully recovered yet. In many ways, common-sense economics was a casualty of this turn. But one of the great conscientious objectors to the excessive formalization of economics was Kenneth Boulding. Boulding was the 2nd winner of the John Bates Clark Medal from the American Economic Association in 1949 (Samuelson was the 1st winner in 1947). Boulding reviewed Samuelson's *Foundations* in the *Journal of Political Economy* in 1948, and as he put it: "Conventions of generality and mathematical elegance may be just as much barriers to the attainment and diffusion of knowledge as may contentment with particularity and literary vagueness.... It may well be that the slovenly and literary borderland between economics and sociology will be the most fruitful building ground during the years to come and that mathematical economics will remain too flawless in its perfection to be very fruitful".

Mathematical reasoning can be a very useful servant to economic theorizing, but it is a horrible master. Economics has suffered from a slavish devotion to mathematical modeling and statistical testing for over 60 years since Boulding wrote he prophetic warning. I hope the young aspiring economists reading this, will take motivation from Bryan Caplan's posts and study the matter seriously. Thinking through the arguments made on both sides, study not only contemporary pronouncements, but trace back the arguments in time to the classic statements by Marshall, Mises, Hayek, Buchanan, Coase, Friedman, Rothbard, Lachmann, and of course Kenneth Boulding.

BTW, Deirdre McCloskey has a wonderful piece on Boulding that you can consult as well.

Boulding is more than misleading here in the language he uses to capture what math can do and what it cannot do, and what language can do that math cannot do.

Language can capture a causal mechanism involving learning, changes in judgment, and open-ended categories and open-ended conceptual change -- math cannot do that.

The issue here is not precision and vagueness, or elegance vs the literary -- distinctions which takes us away from the actual issues at hand.

Literature has nothing to do with with -- just as the hermeneutic/literary metaphor does not help us understand Wittgenstein, logic and language, is does not help,us understand Hayek's explanation of the causal mechanism producing economic order, nor Darwin's explanation of the causal mechanisms of biological order -- both of which are communicated in words.

Posted by: FriedrichHayek | August 24, 2013 at 01:16 PM

Could someone in the know on Rothbard explain what verbal logic has to do with Occam's razor? Is there some kind of implicit assumption here that verbal logic offers the most parsimonious answer? I don't get it.

Posted by: Daniel Kuehn | August 24, 2013 at 03:51 PM

Daniel, the assumption probably is that the models do not add anything in terms of explanation to the verbal reasoning that is behind them and are thus superfluous.

Posted by: Daniil Gorbatenko | August 24, 2013 at 04:23 PM

I would think the opposite would be the case, though, Daniil. Verbal reasoning if anything adds complications to the exposition, right? Given that a problem is amenable to logic in the first place I would think Occam's razor would militate in favor of math.

I'm not sure I'd propose that as a hard rule or anything, but I have no idea why Rothbard seems to be claiming the exact opposite.

Posted by: Daniel Kuehn | August 24, 2013 at 04:38 PM

And there is a difference, I think, between this and saying life is fuzzy and complex and can't be reduced to a logical formulation. To a large extent this IS true and we can't do everything with math or verbal logic.

Posted by: Daniel Kuehn | August 24, 2013 at 04:39 PM

Daniel, you seem to imply that mathematics is some kind of a language that allows to more simply state some ideas. But mathematics isn't a language, the particular notation is. Otherwise mathematical statements couldn't be expressed in words.

I hate to go deep into philosophy but mathematics is a set of concepts with a certain structure of relations among them. As an Aristotelian, I believe that concepts are real. Concepts in this view may only be applied to objects that in some sense contain these concepts. For example, physical objects have length and other mathematical features. It is due to this fact that mathematical models can imperfectly describe the behavior of physical objects.

Now, human decision-making processes and higher-order phenomena arising from them (like prices) do not have mathematical features. Thus, when economic modelers apply mathematical models to them, they, in contrast to physics, use mathematical concepts in their indirect sense, as metaphors. Now since a metaphor is not a concept it may not explain anything in the direct sense of the word, it may only sometimes help grasp the conceptual explanation. It is in this sense that math is superfluous in economics.

Posted by: Daniil Gorbatenko | August 24, 2013 at 07:06 PM

Diran Bodenhorn wrote a great paper on this topic that should be better known IMHO. It includes a devastating critique of a classic in mathematical economics by Harold Hotelling.

The Problem of Economic Assumptions in Mathematical Economics Author(s): Diran Bodenhorn Source: Journal of Political Economy, Vol. 64, No. 1 (Feb., 1956), pp. 25-32 Published by: The University of Chicago Press

Stable URL: http://www.jstor.org/stable/1825857 .

FWIW I never found the quoted Rothbard criticism persuasive. Math can help you describe the initial and final equilibrium and help you identify all the changes you must account for. Verbal reasoning can then help you to figure out what happens to get you from the initial to the final equilibrium. Besides, this bit applies only to a relatively narrow range of mathematical models. For example, how would you apply Rothbard's critique to Arthur's El Farol problem, aka the minority game?

Posted by: Roger Koppl | August 26, 2013 at 07:13 AM

Diran Bodenhorn wrote an excellent piece on mathematical vs. literary economics. It deserves to be better know, indeed a classic. He makes a devastating critique of a classic article by Harold Hotelling.

The Problem of Economic Assumptions in Mathematical Economics Author(s): Diran Bodenhorn Source: Journal of Political Economy, Vol. 64, No. 1 (Feb., 1956), pp. 25-32 Published by: The University of Chicago Press

Stable URL: http://www.jstor.org/stable/1825857 .

Posted by: Roger Koppl | August 26, 2013 at 09:28 AM

OK, so anybody reading this who knows me at all knows that I am way over at the mathy end of this, even beyond Roger. Heck, even though my CV makes no such claim, my Wikipedia entry outright identifies me as a "mathematical economis," period, so I am not going to pretend that I am not, even if that is an overstatement and not really accurate.

So, I do not intend to rehash the basic arguments, which by now I find boring. Yes, math has its limits. Yes, it reguarly gets abused and relied upon to assert things that it either does not prove or are simply tautologically there in the assumptions, the kind of complaint that very-non-Austrian the late Joan Robinson complained about when she said that much of mathematical economic theory amounted to a magician putting a rabbit into a hat in full view of the audience and then expecting them to be all amazed and astounded when the rabbit is pulled back out of the hat.

That said, of course I agree with Roger that some less axiomatic/Bourbakian type approaches such as agent-based modeling, and so on may be useful in ways that the axiomatic approach is not. I have also never been impressed with efforts to denigrate all econometric testing, although I am in sympathy with many critiques of various methods used for this. But the alternative seems to be hand waving while throwing around cherry picked numbers, something really not defensible at all.

My final commment is to pick on Bryan. It may be true at GMU, not known for having lots of highly mathematically oriented economists in its departments, even among the ones not in the Austrian camp, with a few odd exceptions. However, Bryan is simply wrong that when one gives a mathematical economist a mathy paper they only look at the abstract and conclusions. Sure, pretty much anybody will look at the abstract of any paper they are given before they did deeper, but I can asure that real mathematical economists (not necessarily including myself) will generally at least scan the math and certainly figures or graphs and main theorems, if they get past the abstract. Bryan is just out to lunchy on that one (with Tyler and others?).

Posted by: Barkley Rosser | August 26, 2013 at 05:08 PM

BTW, this meme started over on noahpinion, Noah's last post before blowing the popsicle stand, and was picked up by Krugman and others as well, before Bryan got ahold of it, with the thing going all over the place with different people.

Posted by: Barkley Rosser | August 26, 2013 at 05:35 PM

I largely agree with Barkley about fact the agent modeling and econometrics, properly done and understood, have valid roles.

Are there any Austrians who disagree?

I think the Hayek / Austrian conversation on math and data is widely misunderstood.

Posted by: FriedrichHayek | August 27, 2013 at 09:23 PM